The efficiencies of workers P, Q and R are in the ratio 2 : 3 : 4. P and R work on alternate days, while Q works every day. The entire work is completed in 10 days and the total wages for the job are Rs. 1200. Based on their respective contributions, how much money does each of P, Q and R receive?

Introduction / Context:
This time and work question combines worker efficiency with wage distribution. The workers P, Q and R have different efficiencies and do not all work the same days. Since wages are proportional to work done, we first determine each person share of the total work and then allocate the total payment accordingly.

Given Data / Assumptions:
• Efficiency ratio of P : Q : R is 2 : 3 : 4.
• P and R work on alternate days, starting with P on the first day, for a total of 10 days.
• Q works every day for all 10 days.
• Total wages for the work are Rs. 1200.
• Wages are directly proportional to the amount of work done by each worker.

Concept / Approach:
First, convert the efficiency ratio into numerical daily work units. Then calculate total work done by each person over 10 days. The total work is the sum of all contributions. Finally, distribute the total wages in the ratio of work done by P, Q and R, so that each worker is paid fairly according to contribution.

Step-by-Step Solution:
Let the efficiencies of P, Q and R be 2k, 3k and 4k units of work per day respectively. Q works all 10 days, so Q work = 3k × 10 = 30k units. P and R work on alternate days over 10 days, so each of them works on 5 days. P work = 2k × 5 = 10k units. R work = 4k × 5 = 20k units. Total work = 10k + 30k + 20k = 60k units. Shares of work: P : Q : R = 10k : 30k : 20k = 1 : 3 : 2. Total wages = Rs. 1200, so each share = 1200 ÷ (1 + 3 + 2) = 1200 ÷ 6 = Rs. 200. Therefore, P gets 1 share = Rs. 200, Q gets 3 shares = Rs. 600, and R gets 2 shares = Rs. 400.

Verification / Alternative check:
We can verify by adding the three amounts: 200 + 600 + 400 = 1200, which matches the total wage. The ratio 200 : 600 : 400 simplifies to 1 : 3 : 2, which matches the ratio of their total work 10k : 30k : 20k. This confirms that the allocation is consistent with the calculated contributions.

Why Other Options Are Wrong:
Any option that gives R more than Q or P more than Q contradicts their respective total work done. For example, options where P or R receives more than Rs. 600 break the correct 1 : 3 : 2 ratio. Only the distribution Rs. 200, Rs. 600 and Rs. 400 respects both the work ratio and the total sum of Rs. 1200.

Common Pitfalls:
A frequent mistake is to divide wages using only the given efficiency ratio without adjusting for the actual number of days each person works. Another pitfall is to forget that P and R work only 5 days each, while Q works all 10 days. Ignoring this detail leads to an incorrect ratio of contributions and therefore wrong wage allocation.

Final Answer:
P, Q and R receive Rs. 200, Rs. 600 and Rs. 400 respectively.